Karting

Limits, and every number this page quotes

Everything below is measured from the engine that is running on this page, not typed in by hand. The build's page harness (not shipped with the page) re-measures each tagged figure against the engine and fails the build if the page and the physics have drifted apart. Where a number comes from the rule book it is marked; where it is this app's own choice, that is marked too.

What the regulations fix

• Wheelbase 105 cm, inside the 101 to 107 cm the technical regulations allow.
• Front track 110 cm, rear track 114 cm, both at least two thirds of the wheelbase as required, and inside the 140 cm overall width once the tyres are on.
• Wheels 280 mm across the front and 300 mm the rear, with tread 135 mm and 215 mm wide — all four are the maxima for five-inch rims.
• The rear axle is a steel tube 50 mm across with a 1.9 mm wall, which are the limits the regulations set. This app treats it as what it is — a torsion bar — and gets 225 N m per degree out of G J over L and the shear modulus of steel. The two rear wheels ring against it at 120 Hz, and that is the fastest thing in the whole kart.
• Minimum mass 158 kg with the driver aboard, of which the bare kart is at least 75 kg — the figures for the class this kart is built to. A 125 cc two-stroke, limited to 15000 rpm.
• The dry centrifugal clutch starts to bite at 3000 rpm and must be fully home by 5000. Both are quoted from the rule book, not chosen, and they have a consequence: a direct-drive kart bogs off the line, which is why kart races are started rolling.

What this app chose, because nothing published fixes it

• Caster 16° and kingpin inclination 13°, with a scrub radius of 64 mm. No manufacturer publishes a kart's spindle dimensions; these were chosen so the wheel lifts where a kart's lifts.
• Centre of mass 27.8 cm up with 42 % of the weight on the front axle. Calculated from a seated driver, not measured from one.
• Frame torsional stiffness 873 N m per degree by default, adjustable from 384 to 1571. On a real kart you change this with bolt-on stiffener bars; here it is a slider, and it moves the lift threshold.
• The tyre uses the published form of the Magic Formula, but its coefficients are calibrated: the lateral curve peaks at 9.1° of slip angle and the longitudinal one at 12.2 % slip ratio, with a peak friction coefficient of 1.92 at a nominal 420 N. Double that load and it falls to 1.77, which is the whole reason load transfer costs a vehicle grip.
• The circuit is this app's own: 1184 m round, 8 m wide, 10 corners, the tightest of them 18 m, and 10.6 m between its lowest and highest point. No circuit regulation was available to build it to — see below.

What the physics actually produces

• Top speed 117 km/h on the limiter, from a peak of 29.6 hp at 13810 rpm. Nothing sets the top speed; it is where the power meets the drag and the rev limit.
• At full lock the steering lifts the chassis 13.5 mm at the inside front. At a more realistic 10° of lock it is 5.4 mm, and that is enough to move 229 N diagonally across the kart.
• The inside rear wheel leaves the ground at 1.61 g of cornering in a steady corner, and over a flying lap it is in the air 6.7 % of the time.
• While that wheel is down, the locked axle makes a yaw-resisting couple that reaches 508 N m. Fit a differential — which the regulations forbid — and it falls to 15.6, all of which is just the rolling resistance of two unequally loaded tyres.
• The best lap the pace driver has managed is 52.9 s, an average of 80.6 km/h.

How it is checked

• The engine harness runs 1479 assertions with 0 failures.
• The first oracle is a steady-state cornering solver that shares no code and no method with the engine: it writes no differential equation, parametrises the four tyre loads by the front roll moment and pins that with a free-body cut through the frame. Handed nothing but a settled yaw rate and speed, it recovers the steer angle the engine was driven at to 2.8e-12 degrees and all four tyre loads to 7.9e-10 N.
• The second oracle reads no state at all. From an emitted heading trace it puts the inside-rear lift within 0.22° of where the engine's own load says it is, and from five emitted skidpad paths at different ballast it recovers a tyre load exponent of 0.101 against the 0.118 the tyre was built with. Rebuild the tyre linear in load and the same method returns -0.0015, so it is measuring the thing it claims to.
• The physics runs at a fixed 2400 Hz, which is 19.9 samples of that 120 Hz axle mode. The step was measured, not chosen: below about 1000 Hz the error does not grow smoothly, it jumps by four orders of magnitude.

What is wrong with it, or unproven

• There is no published circuit regulation to build to. One would expect the CIK-FIA circuit regulations to fix a minimum track width, a minimum corner radius and a kerb profile. The FIA's own regulations index serves exactly 3 karting PDFs and not one of them is about circuits, and fiakarting.com answers every path with the same 1725-byte JavaScript shell. So the width, the kerbs and the elevation here are invented, and are not claimed to be homologated.
• The load solve is a fixed point, because the loads depend on the very forces the loads produce. It runs 6 passes, which leaves it 0.010 N from converged — measured against the first oracle, not assumed.
• The rear axle is one torsion bar between two wheels. A real kart's sprocket and brake disc sit part-way along it, so the true system is three inertias and two springs, not two and one.
• Tyre temperature, wear and pressure do not exist here. Nor does rain, nor a second kart.
• Combined slip is a friction ellipse laid over two pure-slip curves. That is a defensible construction and it guarantees a tyre at its lateral limit has nothing left for braking, but it is not a measured combined-slip fit, because no such fit is published for a kart slick.
• The chassis is drawn with the heave, pitch, roll and twist the load solve returns, but the frame is drawn rigid: you see the wheel lift, not the rails bending.
• There is no sound.